Torrens is the second Seattle player to land on the virus list in recent days. Outfielder Mitch Haniger was placed on the COVID-19 list on Saturday after he tested positive.
Torrens was placed on the list with Seattle coming off its first day off of the season and ahead of the first game of a series with Texas. Seattle manager Scott Servais said the team's replay coordinator and some other staff are dealing with the virus.
"We had to shuffle some things around here a little bit based on the COIVD situation over the last 24 to 48 hours," Servais said.
Torrens had appeared in four games with three starts this season. He was 3-for-13 at the plate, all singles. Torrens hit .243 with 15 homers and 47 RBIs in 108 games last season.
Seattle selected infielder Mike Ford from Triple-A Tacoma to take Torrens' roster spot. Ford was signed to a minor league contract in March. Ford appeared in 22 games last season for the New York Yankees.